37 citations · 115 across the 22 of their papers we have counts for
7 papers · 1 filter
On the approximation of finite perimeter sets
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna +2
We prove that if is a set with finite perimeter with , then any set of finite perimeter $E\subseteq\m…
Comparison between the non-crossing and the non-crossing on lines properties
Daniel Campbell, Aldo Pratelli, Emanuela Radici
In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions…
Sharp stability for the Riesz potential
Nicola Fusco, Aldo Pratelli
In this paper we show the stability of the ball as maximizer of the Riesz potential among sets of given volume. The stability is proved with sharp exponent , and is valid for…
The property, the boundedness of isoperimetric sets in with density, and some applications
Eleonora Cinti, Aldo Pratelli
We show that every isoperimetric set in R^N with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness resu…
Existence of minimizers for spectral problems
Dario Mazzoleni, Aldo Pratelli
In this paper we show that any increasing functional of the first k eigenvalues of the Dirichlet Laplacian admits a (quasi-)open minimizer among the subsets of R^N of unit measure.…
Existence of isoperimetric regions in with density
Frank Morgan, Aldo Pratelli
We prove the existence of isoperimetric regions in with density under various hypotheses on the growth of the density. Along the way we prove results on the boundedness of i…